Problem: Solve for $x$, ignoring any extraneous solutions: $\dfrac{x^2}{x + 6} = \dfrac{x + 42}{x + 6}$
Explanation: Multiply both sides by $x + 6$ $ \dfrac{x^2}{x + 6} (x + 6) = \dfrac{x + 42}{x + 6} (x + 6)$ $ x^2 = x + 42$ Subtract $x + 42$ from both sides: $ x^2 - (x + 42) = x + 42 - (x + 42)$ $ x^2 - x - 42 = 0$ Factor the expression: $ (x - 7)(x + 6) = 0$ Therefore $x = 7$ or $x = -6$ However, the original expression is undefined when $x = -6$. Therefore, the only solution is $x = 7$.